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2015

Ainsworth, Mark and Barrenechea, Gabriel R. and Wachtel, Andreas (2015) Stabilisation of high aspect ratio mixed finite elements for incompressible flow. SIAM Journal on Numerical Analysis, 53 (2). 1107–1120. ISSN 0036-1429

2013

Ainsworth, Mark and Allendes Flores, Alejandro Ignacio and Barrenechea, Gabriel and Rankin, Richard Andrew Robert (2013) On the adaptive selection of the parameter in stabilized finite element approximations. SIAM Journal on Numerical Analysis, 51 (3). pp. 1585-1609. ISSN 0036-1429

2012

Ainsworth, Mark and Ma, Xinhui (2012) Non-uniform order mixed FEM approximation : implementation, post-processing, computable error bound and adaptivity. Journal of Computational Physics, 231 (2). pp. 436-453. ISSN 0021-9991

Ainsworth, Mark and Allendes Flores, Alejandro Ignacio and Barrenechea, Gabriel and Rankin, Richard Andrew Robert (2012) Computable error bounds for nonconfirming Fortin-Soulie finite element approximation of the Stokes problem. IMA Journal of Numerical Analysis, 32 (2). pp. 414-447. ISSN 0272-4979

Ainsworth, M. and Rankin, R. (2012) Guaranteed computable bounds on quantities of interest in finite element computations. International Journal for Numerical Methods in Engineering, 89 (13). pp. 1605-1634. ISSN 0029-5981

Ainsworth, M. and Rankin, R. (2012) Technical note: a note on the selection of the penalty parameter for discontinuous Galerkin finite element schemes. Numerical Methods for Partial Differential Equations, 28 (3). pp. 1099-1104. ISSN 0749-159X

2011

Ainsworth, Mark and Rankin, Richard Andrew Robert (2011) Realistic computable error bounds for three dimensional finite element analyses in linear elasticity. Computer Methods in Applied Mechanics and Engineering, 200 (21-22). pp. 1909-1926. ISSN 0045-7825

Ainsworth, Mark and Andriamaro, Miangaly Gaelle and Davydov, Oleg (2011) Bernstein–Bézier finite elements of arbitrary order and optimal assembly procedures. SIAM Journal on Scientific Computing, 33 (6). pp. 3087-3109. ISSN 1064-8275

Ainsworth, Mark and Rankin, Richard Andrew Robert (2011) Constant free error bounds for nonuniform order discontinuous Galerkin finite-element approximation on locally refined meshes with hanging nodes. IMA Journal of Numerical Analysis, 31 (1). pp. 254-280. ISSN 0272-4979

Ainsworth, Mark and Vejchodsky, Tomas (2011) Fully computable robust a posteriori error bounds for singularly perturbed reaction–diffusion problems. Numerische Mathematik, 119 (2). pp. 219-243. ISSN 0029-599X

2010

Ainsworth, Mark and Rankin, R. (2010) Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity. International Journal for Numerical Methods in Engineering, 82 (9). pp. 1114-1157. ISSN 0029-5981

Ainsworth, M. and Wajid, Hafiz Abdul (2010) Optimally blended spectral-finite element scheme for wave propagation and nonstandard reduced integration. SIAM Journal on Numerical Analysis, 48 (1). pp. 346-371. ISSN 0036-1429

Ainsworth, M. and Rankin, R. (2010) Fully computable error bounds for discontinuous Galerkin finite element approximations on meshes with an arbitrary number of levels of hanging nodes. SIAM Journal on Numerical Analysis, 47 (6). pp. 4112-4141. ISSN 0036-1429

Ainsworth, Mark and Wajid, Hafiz Abdul Support of MA by the Engineering and Physical Sciences Research Council under grant (Funder) (2010) Explicit discrete dispersion relations for the acoustic wave equation in d-dimensions using finite element, spectral element and optimally blended schemes. In: Computer Methods in Mathematics. Computer Methods in Mathematics: Advanced Structured Materials, 1 (1). Springer, pp. 3-17.

Ainsworth, M. (2010) A framework for obtaining guaranteed error bounds for finite elements approximations. Journal of Computational and Applied Mathematics, 234 (9). pp. 2618-2632. ISSN 0377-0427

2009

Mihai, L. Angela and Ainsworth, Mark (2009) A finite element procedure for rigorous numerical enclosures on the limit load in the analysis of multibody structures. Computer Methods in Applied Mechanics and Engineering, 199 (1-4). pp. 48-60.

Ainsworth, M. and Mihai, L.A. (2009) An adaptive multi-scale approach to the modelling of masonry structures. International Journal for Numerical Methods in Engineering, 78 (10). pp. 1135-1163. ISSN 0029-5981

Mihai, L.A. and Ainsworth, M. (2009) An adaptive multi-scale computational modelling of Clare College Bridge. Computer Methods in Applied Mechanics end Engineering, 198 (21-26). pp. 1839-1847. ISSN 0045-7825

Ainsworth, M. and Demkowicz, L. (2009) Explicit polynomial preserving trace liftings on a triangle. Mathematische Nachrichten, 282 (5). pp. 640-658. ISSN 0025-584X

Ainsworth, Mark and Wajid, Hafiz Abdul (2009) Dispersive and dissipative behavior of the spectral element method. SIAM Journal on Numerical Analysis, 47 (5). pp. 3910-3937. ISSN 0036-1429

2008

Ainsworth, M. and Rankin, R. (2008) Fully computable bounds for the error in nonconforming finite element approximations of arbitrary order on triangular elements. SIAM Journal on Numerical Analysis, 46 (6). pp. 3207-3232. ISSN 0036-1429

Ainsworth, M. and Rankin, R. (2008) Robust a posteriori error estimation for the nonconforming fortin-soulie finite element approximation. Mathematics of Computation, 77 (264). pp. 1917-1939. ISSN 0025-5718

2005

Dörfler, W. and Ainsworth, M. (2005) Reliable a posteriori error control for non-conforming finite element approximation of Stokes flow. Mathematics of Computation, 74 (252). pp. 1599-1619. ISSN 0025-5718

Ainsworth, M. (2005) Robust a posteriori error estimation for non-conforming finite element approximation. SIAM Journal on Numerical Analysis, 42 (6). pp. 2320-2341.

Ainsworth, M. (2005) A posteriori error estimation for non-conforming quadrilateral finite elements. International Journal of Numerical Analysis and Modeling, 2 (1). pp. 1-18. ISSN 1705-5105

2004

Ainsworth, M. (2004) Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods. Journal of Computational Physics, 198 (1). pp. 106-130. ISSN 0021-9991

Ainsworth, Mark (2004) Dispersive properties of high order nedelec/edge element approximation of the time-harmonic Maxwell equations. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 362 (1816). pp. 471-493. ISSN 1471-2962

Ainsworth, M. (2004) Discrete dispersion relation for hp-version finite element approximation at high wave number. SIAM Journal on Numerical Analysis, 42 (2). pp. 553-575. ISSN 0036-1429

Ainsworth, M. (2004) Review of Adaptive Finite Element Methods for Differential Equations by W Bangerth and R Rannacher. SIAM Review, 46 (2). pp. 354-356. ISSN 0036-1445

2003

Ainsworth, M. and Coyle, J. (2003) Hierarchic finite element bases on unstructured tetrahedral meshes. International Journal for Numerical Methods in Engineering, 58 (14). pp. 2103-2130. ISSN 0029-5981

Ainsworth, M. and Coyle, J. and Ledger, P. and Morgan, K. (2003) Computation of Maxwell eigenvalues using higher order edge elements in three dimensions. IEEE Transactions on Magnetics, 39 (5). pp. 2149-2153. ISSN 0018-9464

Ainsworth, M.; Cohen, Gary and Heikkola, Erkki and Joly, Patrick and Neittaanmäki, P., eds. (2003) Dispersive properties of high order finite elements. In: Mathematical and numerical aspects of wave propagation waves 2003. Springer, London, UK, pp. 3-11. ISBN 354040127X

Ainsworth, M. and McLean, W. (2003) Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes. Numerische Mathematik, 93 (3). pp. 387-413. ISSN 0029-599X

Ainsworth, M. and Coyle, J. (2003) Conditioning of hierarchic p-version Nedelec elements on meshes of curvilinear quadrilaterals and hexahedra. SIAM Journal on Numerical Analysis, 41 (2). pp. 731-750. ISSN 0036-1429

Ainsworth, M. (2003) Topics in Computational Wave Propagation: Direct and Inverse Problems. Lecture Notes in Computational Science and Engineering . Springer. ISBN 3-540-00744-X

Ainsworth, M. (2003) Workshop at Newton Institute Heralds Programme on Computational Challenges in PDEs. Isaac Newton Institute for Mathematical Sciences, Cambridge, UK.

Ainsworth, M. and Pinchedez, K. (2003) hp-Approximation theory for BDFM/RT finite elements and applications. SIAM Journal on Numerical Analysis, 40 (6). pp. 2047-2068. ISSN 0036-1429

2002

Ainsworth, M. and Coyle, J.; Brezzi, F. and Buffa, Anthony J. and Corsaro, S. and Murli, A., eds. (2002) Computation of Maxwell eigenvalues on curvilinear domains using hp-version nedelec elements. In: Numerical mathematics and advanced applications. Springer, Italy. ISBN 8847001803

Ainsworth, M. and Coggins, P. (2002) A uniformly stable family of mixed hp-finite elements with continuous pressures for incompressible flow. IMA Journal of Numerical Analysis, 22 (2). pp. 307-327. ISSN 0272-4979

Ainsworth, M. and Guo, B. (2002) Analysis of iterative sub-structuring techniques for boundary element approximation of the hypersingular operator in three dimensions. Applicable Analysis, 81 (2). pp. 241-280. ISSN 0003-6811

Ainsworth, M. and Pinchedez, K. (2002) The HP-MITC finite element method for the Reissner-Mindlin Plate Problem. Journal of Computational and Applied Mathematics, 148 (2). pp. 429-462. ISSN 0377-0427

2001

Ainsworth, Mark and Kelly, Donald W. (2001) A posteriori error estimators and adaptivity for finite element approximation of the non-homogeneous dirichlet problem. Advances in Computational Mathematics, 15 (1-4). pp. 3-23. ISSN 1019-7168

Ainsworth, Mark and Coyle, Joe (2001) Hierarchic hp-edge element families for Maxwell's equations on hybrid quadrilateral/triangular meshes. Computer Methods in Applied Mechanics and Engineering, 190 (49-50). pp. 6709-6733.

Ainsworth, M. (2001) Essential boundary conditions and multi-point constraints in finite element analysis. Computer Methods in Applied Mechanics and Engineering, 190 (48). pp. 6323-6339.

Ainsworth, Mark (2001) Review of p and hp-finite element methods. Theory and applications in solid and fluid mechanics. Mathematics of Computation, 70 (235). pp. 1335-1337. ISSN 0025-5718

Ainsworth, Mark and Dörfler, Willy (2001) Fundamental systems of numerical schemes for linear convection diffusion equations and their relationship to accuracy. Computing, 66 (2). pp. 199-229. ISSN 0010-485X

Ainsworth, Mark and Arnold, Mark E. (2001) Computable error bounds for some simple dimensionally reduced models on thin domains. IMA Journal of Numerical Analysis, 21 (1). pp. 81-105. ISSN 0272-4979

Ainsworth, M. and Coyle, J. (2001) hp-finite element approximation of Maxwell's equations on curvilinear hybrid meshes. In: European Conference on Computational Mechanics, 2001-06-26 - 2001-06-29.

Ainsworth, M. and Melboe, H. (2001) A posteriori error estimation for anisotropic finite elements. In: European Conference on Computational Mechanics, 2001-06-26 - 2001-06-29.